Question: Rewrite as a simplified fraction. ${0.34\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 346.6666...\\ 100x &= 34.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 312}$ ${x = \dfrac{312}{900}} $ ${x = \dfrac{26}{75}} $